The Beta Reputation System

1. The Beta Reputation System AudunJøsang and Roslan Ismail [1] Presented by Hamid Al-Hamadi CS 5984, Trust and Security, Spring 2014

2. Outline • Introduction • Building Blocks in the Beta Reputation System • Performance of the Beta Reputation System • Conclusion

3. Introduction • Many existing reputation systems • Applicability in e-commerce systems: • Enforcement is needed in order for contracts and agreements to be respected • Traditionally rely on legal procedures to rectify disagreement. • Hard to enforce in e-commerce • unclear which jurisdiction applies • cost of legal procedures

4. Introduction • Reputation systems • As a substitute to traditional Reputation systems can be used to encourage good behavior and adherence to contracts • Fostering trust amongst strangers in e-commerce transactions • Gathers, distributes, and aggregates feedback about participants behavior • Incentive for honest behavior and help people make decisions about who to trust. • Without a reputation system taking account past experiences, strangers might prefer to act deceptively for immediate gain instead of behaving honestly.

5. Introduction • Online auction sites were the first to introduce reputation schemes e.g. eBay.com • Others include company reputation rating sites such as BizRate.com, which ranks merchants on the basis of customer ratings • The internet is efficient in capturing and distributing feedback, unlike the physical world. • Some challenges: • An entity can attempt to change its identity to erase prior Feedback • Restart after it builds a bad reputation • Not enough feedback provided by surrounding entities • Negative feedback hard to elicit • Difficult to ensure feedback is honest

6. Introduction • Example of dishonesty through reputation systems: • Three men attempt to sell a fake painting on eBay for $US135,805 • Two of the fraudsters actually had good Feedback Forum ratings as they rated each other favorably and engaged in honest sales prior to fraudulent attempt. • Sale was abandoned just prior to purchase, buyer became suspicious

7. Introduction • Fundamental aspects: • Reputation engine • Calculates users’ reputation ratings are from various inputs including feedback from other users • Simple or complex mathematical operations • Propagation mechanism • Allows entities to obtain reputation values • Two approaches: • Centralized (e.g. eBay) • Reputation values are stored in a central server • Users forward their query to the central server for the reputation value whenever there is a need • Decentralized • Everybody keeps and manages reputation of other people themselves • Users can ask others for the required reputation values

8. Introduction • Authors propose a new reputation engine based on the beta probability density function called the beta reputation system • strongly based on theory of statistics • paper describes centralized approach, but the reputation system can also be used in a distributed setting

9. Building Blocks in the Beta Reputation System • The Beta Density Function • Can be used to represent probability distributions of binary events • The beta-family of probability density functions is a continuous family of functions indexed by the two parameters α and β .

10. Building Blocks in the Beta Reputation System • “When observing binary processes with two possible outcomes , the beta function takes the integer number of past observations of and to estimate the probability of , or in other words, to predict the expected relative frequency with which will happen in the future.”

11. Building Blocks in the Beta Reputation System

12. Building Blocks in the Beta Reputation System • Example: • process with two possible outcomes • Produced outcome 7 times • Produced outcome 1 time • Will have beta function as plotted below:

13. Building Blocks in the Beta Reputation System • Example (cont’): • represents the probability of an event • Curve represents the uncertain probability that the • process will produce outcome • during future observations • represents the • probability that the first-order variable has a specific value • probability expectation value -> the most likely value of the relative frequency of outcome is 0.8 8 / (8 + 2)

14. Building Blocks in the Beta Reputation System • The Reputation Function • In e-commerce an agent’s perceived satisfaction after a transaction is not binary - not the same as statistical observations of a binary event. • Let positive and negative feedbacks be given as a pair • of continuous values. Degree of satisfaction Degree of dissatisfaction

15. Building Blocks in the Beta Reputation System Compact notation :

16. Building Blocks in the Beta Reputation System • T’s reputation function by X is subjective (as seen by X) Superscript (X): feedback provider Subscript (T): feedback target

17. Building Blocks in the Beta Reputation System • The Reputation Rating • Simpler representation to communicate to humans that a reputation function • Given as a probability value – within a range • Neutral value is in middle of range • Scale the rating to be in the range [-1,+1] • A measure of reputation and how an entity is expected to behave in the future

18. Building Blocks in the Beta Reputation System • Combining Feedback • Can combine positive and negative feedback from multiple sources e.g. combine feedback from X and Y about target T Combine positive feedback Combine negative feedback Operation is both commutative and associative

19. Building Blocks in the Beta Reputation System • Discounting • Used to vary the weight of the feedback based on the agents reputation • Described in the context of belief theory • Jøsang’s belief model uses a metric called opinion to describe beliefs about the truth of statements • interpreted as probability that proposition x is true • interpreted as probability that proposition x is false • interpreted as inability to assess the probability value of x

20. Building Blocks in the Beta Reputation System • Y has opinion about T, gives it to X • X has opinion about Y • Then X can express its opinion about T taking into account its opinion about Y’s advice • , as follows: Given by Y (its opinion about T) Apply X’s opinion about Y

21. Building Blocks in the Beta Reputation System • The opinion metric can be interpreted equivalently to the beta function • mapping between the two representations defined by: • Using previous eq., discounting operator for reputation functions is obtained: Associative but not commutative

22. Building Blocks in the Beta Reputation System • Forgetting • Old feedback less relevant for actual reputation rating • Behavior changes over time • Old feedback is given less weight than new feedback • Can use an adjustable forgetting factor Order of feedback processing matters • If λ=1 -> no forgetting factor, nothing is forgotten • If λ=0 -> only last feedback, all others forgotten

23. Building Blocks in the Beta Reputation System • Forgetting (cont’) • To avoid saving all of the feedback tuples (Q) forever, a recursive • algorithm can be used instead:

24. Building Blocks in the Beta Reputation System • Providing and collecting feedback: • After each transaction, a single agent can provide both positive • and negative feedback simultaneously: • Feedback can be partly satisfactory, and given as a pair • The sum can be interpreted as the weight of the feedback • Minimum weight of feedback is r + s = 0, equivalent to not providing • feedback • Alternatively, define a normalization weight denoted by so that the • sum of the parameters satisfy • Feedback can be provided as a single value with values within a specified • range • If we have such that then the can be derived • using and as follows: • Weight can reflect importance of transactions (high importance -> high )

25. Building Blocks in the Beta Reputation System • Feedback is received and stored by a feedback collection centre C • Assumed that all agents are authenticated and that no agent can change identity • Agents provide feedback about transaction • C discounts received feedback based on providers reputation and updates the • target’s reputation function and rating accordingly • C provides updated reputation ratings to requesting entities

26. Performance • Example A: Varying Weight • This example shows how the reputation rating evolves as a function • of accumulated positive feedback with varying weight w • Let C receive a sequence Q of n identical feedback values v=1 about target T • Then: Reputation parameters: Reputation rating: Derived from previous equations:

27. Performance w=1 w=0

28. Performance • Example B: Varying Feedback • This example shows how the reputation rating evolves as a function of accumulated feedback with fixed weight w = 1 and varying feedback value v V=1 • For v=1 the rating approaches 1, • and for v=-1 the rating • approaches -1. V=-1

29. Performance • Example C: Varying Discounting • This example shows how the reputation rating evolves as a function of accumulated feedback with fixed weight w = 1 and varying discounting • C receives a sequence Q of n identical feedback values v =1 about target T • Forgetting is not considered • Each feedback tuple with fixed value (1, 0) is discounted based on the feedback provider’s reputation function defined by Reputation parameters: Reputation rating:

30. Performance • Example C: Varying Discounting (cont’) practically equivalent to no discounting at all Varying Feedback provider’s reputation function parameters • As X’s reputation function gets weaker T’s rating is less influenced by the feedback From X • with r=0, s=0 , T’s rating not influenced by X’s rating

31. Performance • Example D: Varying Forgetting Factor • This example shows how the reputation rating evolves as a function of accumulated feedback with fixed weight w = 1 and varying forgetting factor λ • C receives a sequence Q of n identical feedback values v =1 about target T • Discounting is not considered • Using previous equations, the reputation parameters and rating can be expressed as a function of n and λaccording to:

32. Performance • Example D: Varying Forgetting Factor (cont’)

33. Performance • Example E: Varying Feedback and Forgetting Factor • This example shows how the reputation rating evolves as a function of accumulated feedback with fixed weight w = 1. • Let there be a sequence Q of 50 feedback inputs about T, where the first 25 have value , and the subsequent 25 inputs have value • Using previous equations, the reputation parameters and rating can be expressed as a function of n, v, and λaccording to: In more explicit form:

34. Performance • Example E: Varying Feedback and Forgetting Factor (cont’) In more explicit form:

35. Performance • Example E: Varying Feedback and Forgetting Factor (cont’) v=1 v=-1 • Two phenomena can be observed when the forgetting factor is low (i.e. when feedback is quickly forgotten): • Firstly the reputation rating reaches a stable value more quickly, and • secondly the less extreme the stable reputation rating becomes.

36. Conclusion • Reputation systems can be used to encourage good behavior and adherence to contracts in e-commerce • Authors propose a beta reputation system which is based on using beta probability density functions to combine feedback and derive reputation ratings • Strong foundation on the theory of statistics • Assumed a centralized approach, although it is possible to adapt the beta reputation system in order to become decentralized • flexibility and simplicity makes it suitable for supporting electronic contracts and for building trust between players in e-commerce

37. References [1] A. Josang, and R. Ismail, "The Beta Reputation System,” 15th Bled Electronic Commerce Conference, Bled, Slovenia, June 2002, pp. 1-14.